## ABout the workshop

This 3-day workshop aims to promote state-of-the art mathematical biology researches in the Philippines. It is expected to stimulate young mathematicians of possible inter-disciplinary research directions in mathematics and biology. This activity is envisioned to provide an opportunity for local researchers to establish research collaborations within the country, and between the Philippines and developed countries. It brings together local enthusiasts in the field serving as a focal group to build a mathematical biology community eventually leading to the establishment of a professional organization.

This is the first workshop in the Philippines that will convene local mathbio researchers and foreign experts working in a wide range of researches at the interface of mathematics and life sciences including population dynamics, ecology, developmental biology, biophysics, epidemiology, physiology, etc. Workshop activities include plenary and invited talks, round table discussions and student presentations (oral and poster). It features a mini-project designed for graduate students to spur active participation. Prior to the activity, references and relevant materials regarding the mini-project will be disseminated. Students will be grouped into 4 or 5 on the first day and have the results presented on the last day. While the students are working on the project, local researchers together with the foreign experts will have a round table discussion on the current status and possible outlook of mathematical biology community in the country. Proposals and suggestions on how to move forward as a formal group are expected and probable challenges will be discussed.

This will be a major event in the Philippines in celebration of the

This is the first workshop in the Philippines that will convene local mathbio researchers and foreign experts working in a wide range of researches at the interface of mathematics and life sciences including population dynamics, ecology, developmental biology, biophysics, epidemiology, physiology, etc. Workshop activities include plenary and invited talks, round table discussions and student presentations (oral and poster). It features a mini-project designed for graduate students to spur active participation. Prior to the activity, references and relevant materials regarding the mini-project will be disseminated. Students will be grouped into 4 or 5 on the first day and have the results presented on the last day. While the students are working on the project, local researchers together with the foreign experts will have a round table discussion on the current status and possible outlook of mathematical biology community in the country. Proposals and suggestions on how to move forward as a formal group are expected and probable challenges will be discussed.

This will be a major event in the Philippines in celebration of the

*.***Year of Mathematical Biology**## PROJECT DESCRIPTION

**Project 1: Pattern formation for animal coats using the phase-field methods**

**Supervisor : Seunggyu Lee**

The phase-field model has a various applications in scientific and engineering fields such as spinodal decomposition, diblock copolymer, tumor growth, cell cytokinesis, image inpainting, multiphase fluid flows, and etc. It is a kinds of interface capturing methods using a partial differential equation; therefore, the interface can be easily represented when it is too complex or has topological change. In Sander and Wanner's work (J. Differ. Equations 2003), they discussed that the mechanism for the Cahn-Hilliard equation, the governing equation of the phase-field method, is responsible for the pattern formation for animal coats using the reaction-diffusion models. Actually, it has been an interesting issue understanding and explaining the animal coat pattern formation for both biologists and mathematicians.

In this project, we will briefly study the phase-field model and apply it to model the pattern formation for animal coats. The aim is the parameter study to investigate many of the commonly occuring pattern types observed in animal skins and, if possible, modify the models to find new patterns. This project may be ideal for students who have an interest in mathematical modeling based on a partial differential equation, scientific computing, and biological patterns.

Recommended literature:

[1] D. Jeong, J. Shin, Y. Li, Y. Choi, J.-H. Jung, S. Lee, J. Kim,

[2] S. Kondo, T. Miura,

In this project, we will briefly study the phase-field model and apply it to model the pattern formation for animal coats. The aim is the parameter study to investigate many of the commonly occuring pattern types observed in animal skins and, if possible, modify the models to find new patterns. This project may be ideal for students who have an interest in mathematical modeling based on a partial differential equation, scientific computing, and biological patterns.

Recommended literature:

[1] D. Jeong, J. Shin, Y. Li, Y. Choi, J.-H. Jung, S. Lee, J. Kim,

*Numerical analysis of energy-minimizing wavelengths of equilibrium states for diblock copolymers*, Current Applied Physics 14 (2014) 1263-1272.[2] S. Kondo, T. Miura,

*Reaction-Diffusion model as a framework for understanding biological pattern formation*, Science 329 (2010) 1616-1620.**Project 2: An introduction to metapopulation models for infectious diseases**

**Supervisor : Jonggul Lee**

Transmission dynamics of infectious diseases is a localized process. For directly transmitted diseases, for example, transmission is most likely between individuals with most intense interaction which implies those in the same location in general. Movement of individuals between populations facilitates the geographical spread of infectious diseases. In this workshop we are going to concern with capturing these host population characteristics and address following issues:

Recommended literature:

[1] van den Driessche, P. (2008).

[2] Hyman, J. M. and Laforce, T. (2003).

[3] Lloyd, A. L. and Jansen, V. A. A. (2004).

- Determining the rate of spatial transmission of a pathogen
- Calculating the influence of demographic effects on interactions between host populations
- Finding optimally targeted control measures that consider the local nature of spatial transmission

*metapopulation*models describe disease spread on a number of spatial patches. They usually consist of a system (often a large system) of ordinary differential equations with the dynamics of each patch coupled to that of other patches by travel. A patch can be a city, community, or some other geographical region. To illustrate key issues, such as scale of host populations and their interactions, several types of metapopulation models from the literature will be considered in this project. But since these models can be complicated, participants are asked to consult the following references for more background and details.Recommended literature:

[1] van den Driessche, P. (2008).

*Spatial structure: Patch models. In Mathematical Epidemiology*(Vol. 1945, pp. 179–189).[2] Hyman, J. M. and Laforce, T. (2003).

*Modeling the spread of influenza among cities*. Bioterrorism: Mathematical Modeling Applications in Homeland Security, 28: 211.[3] Lloyd, A. L. and Jansen, V. A. A. (2004).

*Spatiotemporal dynamics of epidemics: Synchrony in metapopulation models.*Mathematical Biosciences, 188(1–2): 1–16.**Project 3: An introduction to optimal control problems in epidemic models**

**Supervisors : Sunhwa Choi and Soyoung Kim**

Mathematical modeling is an important tool for not only describing the dynamics of the spread of an infectious disease but also analyzing the effect of interventions on its dynamics. Since many types intervention controls and its combinations are conducting in real world, it is necessary to compare and analyze the effects of the intervention controls. Mathematical model can be particularly useful in comparing the effect of various prevention, therapy and control programs.

Optimal control theory in the infectious disease modeling is a widely used method to suggest the best intervention scenario to mitigate the disease spread. In order to reflect the real situation better, design optimal control problems in terms of some pre-assumed criterion based on the specific circumstances is important.

In this project, we serves as an introduction to optimal control theory applied to system of ordinary differential equations (ODEs) with emphasis on disease models.

The project focuses on suggestion the intervention strategies in order to mitigate the spread of infectious diseases using optimal control theory using simple models: Susceptible-Infectious- Recovered (SIR) and Susceptible-Infectious-Susceptible (SIS) models. Two models (SIS and SIR) are used to compare the differences in intervention strategies, depending on the model.

Recommended literature:

R. M. Neilan and S. Lenhart,

Optimal control theory in the infectious disease modeling is a widely used method to suggest the best intervention scenario to mitigate the disease spread. In order to reflect the real situation better, design optimal control problems in terms of some pre-assumed criterion based on the specific circumstances is important.

In this project, we serves as an introduction to optimal control theory applied to system of ordinary differential equations (ODEs) with emphasis on disease models.

The project focuses on suggestion the intervention strategies in order to mitigate the spread of infectious diseases using optimal control theory using simple models: Susceptible-Infectious- Recovered (SIR) and Susceptible-Infectious-Susceptible (SIS) models. Two models (SIS and SIR) are used to compare the differences in intervention strategies, depending on the model.

Recommended literature:

R. M. Neilan and S. Lenhart,

*An Introduction to Optimal Control with an Application in Disease Modeling,*Modeling Paradigms and Analysis of Disease Trasmission Models 2010: 67-82.**Project 4: Can we use Michaelis-Menten or Hill type functions for stochastic simulations?**

**Supervisor : Jae Kyoung Kim**

Biological systems evolve in disparate timescales. For instance, dimerization of proteins occur much faster than the translation of protein. Birth or death rates of subjects is often much lower than the infection rate. In such case, the quasi-steady-state approximation (QSSA) utilizes timescale separation to simplify the deterministic models via nonelementary reaction-rate functions (e.g., Michaelis-Menten or Hill functions). These deterministically reduced model based on the nonelementary functions have also been widely used for stochastic simulations (e.g using Michaelis-Menten or Hill functions for the propensity functions of Gillespie algorithm). However, this approach is not always accurate and often leads enourmous errors. In this project, we will learn under which condition we can use the nonelementary functions for the stochastic simulations with Gillespie algorithm.

Main reference:

Kim JK, Josic K, and Bennett MR, The relationship between deterministic and stochastic quasi steady state approximation, BMC Systems Biology 9:87(2015) Figure 1.

Optional reference:

Kim JK, Sontag E, Reduction of Multiscale Stochastic Biochemical Reaction Networks using Exact Moment Derivation, PLoS Compuational Biology (2017)

Kim JK, Josic K, and Bennett MR, The validity of quasi steady-state approximations in discrete stochastic simulations, Biophysical Journal 107 (2014)

Main reference:

Kim JK, Josic K, and Bennett MR, The relationship between deterministic and stochastic quasi steady state approximation, BMC Systems Biology 9:87(2015) Figure 1.

Optional reference:

Kim JK, Sontag E, Reduction of Multiscale Stochastic Biochemical Reaction Networks using Exact Moment Derivation, PLoS Compuational Biology (2017)

Kim JK, Josic K, and Bennett MR, The validity of quasi steady-state approximations in discrete stochastic simulations, Biophysical Journal 107 (2014)

**Project 5: Introduction and application of a lumped parameter model of the cardiovascular system**

**Supervisor : Wanho Lee**

In this project we will treat a mathematical model of pumping heart coupled to lumped compartments of blood circulation. Our model consists of eight compartments of the body as simple as possible that include pumping heart, the systemic circulation, and the pulmonary circulation. The governing equations for the pressure and volume in each vascular compartment are derived from the following equations:

(Ohm's law)

(Conservation of volume)

(Definition of compliances)

where P is blood pressure, Q is blood flow, R is resistance, V is volume and C is compliance.

The pumping source is modeled by the time-dependent linear curves from physiological relation in the heart. We show that the numerical results in normal case are in agreement with corresponding data found in the literature. We extend the developed lumped model of circulation in normal case into a specific model for arrhythmia. These models provide valuable tools in examining and understanding cardiovascular diseases.

References

[1] Jung, E., & Lee, W. (2006). Lumped parameter models of cardiovascular circulation in normal and arrhythmia cases.

[2] Hoppensteadt, F. C., & Peskin, C. S. (2002).

(Ohm's law)

(Conservation of volume)

(Definition of compliances)

where P is blood pressure, Q is blood flow, R is resistance, V is volume and C is compliance.

The pumping source is modeled by the time-dependent linear curves from physiological relation in the heart. We show that the numerical results in normal case are in agreement with corresponding data found in the literature. We extend the developed lumped model of circulation in normal case into a specific model for arrhythmia. These models provide valuable tools in examining and understanding cardiovascular diseases.

References

[1] Jung, E., & Lee, W. (2006). Lumped parameter models of cardiovascular circulation in normal and arrhythmia cases.

*Journal of the Korean Mathematical Society*,*43*(4), 885-897.[2] Hoppensteadt, F. C., & Peskin, C. S. (2002).

*Modeling and simulation in medicine and the life sciences, second edition*, Chapter 1. Springer Science & Business Media.## Programme

## How to get to venue

*Under construction*